APPENDIX A
ALTERNATIVE METHOD OF FINDING THE COORDINATES OF JOINT C
A.1 Subchain (R-L)-R-S
By using the notations as shown in Fig. A.1 and the
method presented in [44], we can obtain the coordinates of
joint C with respect to the local coordinate system as
R = Sl1l + a12a12 + S22S2 + a23a23 (A.I)
where S1 is the translation along the S1 axis, S22 is the
offset along the 12 axis, and a12 and a23 are the
perpendicular distances between successive joint axes.
We can rewrite Eq. (A.1) by using the Table A.1 (set 1
of direction cosines spatial heptagon) as follows:
r I
S c -s1 0 0 1 0
R = sI cl 0 { S1 0 + al2 0 + S22 -s12
0 0 1 1 0 c12
r 1
I 2
I 21 (A.2)
+ a23 U21 }(A.2
where U21 = s2c12 and U21 = s2s12*
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